Review of Differentiation, Math 223

Find the first derivatives of the following functions. Use proper notation.

1. $f(x)=\frac{x^2+bx+c}{a}$2. $y(t)=\frac{3}{\sqrt{t}+2}$3. $z = \frac{\sec(w)}{1 + \tan(w)}$
4. $f(x)=x^2\cos(x)+3\sin(4)$5. $v=\sqrt[3]{\tan(5t)}$6. $t(y)=\left(\frac{y-5}{2y+1}\right)^3$
7. $y(\theta)=\ln (\sin(\pi \theta))$8. $f(t)=\exp(1/t)$9. $f(\theta)=e^{-\theta}\cos(b\theta)$
10. $z=5^{\sin(x)}$11. $y = \frac{1}{\arctan(x)}$12. $f(t)=\arcsin(t^2)$
13. $v(r)=\pi^r \cdot r^\pi$14. $y = e^{\sqrt{x}}(x^2+1)$15. $z=\log(10^{2x})$
16. $f(m)=\frac{1}{\sec(2m)}$17. $f(\Gamma)=\frac{\beta \Gamma + \Gamma^6}{1 - \beta}$18. $s = \frac{\ln (t)}{1 + \ln(t)}$
19. $y = \frac{x^3}{(1-x)^2}$20. $f(t) = \frac{\sqrt{t}+4}{t}$21. $y=e^{\ln(x+1)}$



Vector Calculus
1999-01-29